Question: Subtract $3x^2+7x-4$ from $8x^2-6x+2$.
Answer: Since we are asked to subtract $3x^2+7x-4$ from $8x^2-6x+2$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $3$ from $10$ ", we would rewrite it as $10 - 3$. In other words, we would start with $10$ and then subtract $3$. Let's use this pattern to rewrite the problem as one expression: ${(8x^2-6x+2)-(3x^2+7x-4)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(8x^2-6x+2){-}(3x^2+7x-4)\\ \\ =&(8x^2-6x+2){-}3x^2{-}7x{-}(-4)\\ \\ =&8x^2-6x+2-3x^2-7x+4 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${x^2}, {x},$ and the $\text{{constant}}$ term: ${{8x^2} {-6x} {+2} {-3x^2} {-7x} {+4}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(8-3)x^2} + {(-6-7)x} + {(2+4)}}$ When we combine the coefficients in front of each term, we get the following trinomial: $5x^2 -13x + 6$